While coffee is acidic, those acids are largely removed in the brewing process (and are part of the beneficial health aspect of a cup of coffee). This results in the spent grounds having a neutral pH balance, which means they can be a helpful soil amendment for plants since the grounds are not acidic. These spent coffee grounds also contain nitrogen (although they do not initially function as a plant fertilizer).
They can also be used to help control weeds as a key mulch component. And there are even reports that they help to deter slugs and snails.
It appears that if used appropriately, recycled coffee grounds (which can incorporate the paper filters as well) potentially have a health benefit for native plant gardens that may approach the health benefit we derive from drinking the liquid brewed from those grounds. And those recycled grounds don't add to the size of your local landfill.
Cochran, DR, PR Knight and M Gu. 2014. Effect of spent coffee grounds on germination of palmer amaranth, perennial rye, and white clover. SNA Research Conference Vol. 56 2011. Available on-line at: http://www.slideshare.net/v2zq/weed-control-effect-of-spent-coffee
This study found that mulching with spent coffee grounds (SCG) resulted in fewer white clover seedlings and that is also provided an organic alternative to the use of herbicides in the container nursery industry.
Malhi, HS. 2001. Weed suppression through three mulches (subterranean clover, coffee grounds, newspaper/straw mix) on a swiss beet chard crop. ES Senior Thesis Project. University of California, Berkeley. Available on-line at: http://nature.berkeley.edu/classes/es196/projects/2001final/Malhi.pdf
This conclusion of this thesis was while it was not as effective as newspaper and straw mixed (and was also more labor intensive than the foregoing), that coffee grounds can be effectively used to suppress weeds, and can often be obtained in quantity for free.
NOTE: none of the foregoing applies to single-serve cups of coffee, i.e. so-called coffee pods or K-cups (in particular the plastic kind). These are harmful to the environment and should be avoided.
Suggestion: initially try adding spent coffee grounds to just a few, small areas in your garden to assess their effectiveness before widespread use.
Warning/other considerations: the possible impact to a dog, cat or wildlife consuming a large amount of spent coffee grounds should be considered since some level of toxicity is possible depending on how much is consumed. For this reason, it is probably not a good idea to simply spread the coffee grounds on top of the soil without working them into the soil to some degree, or without first mixing them with soil or some other additive, and not maintaining soils depths containing coffee grounds of more than say a few inches. Compost piles or containers in which the coffee grounds are kept should be tightly secured or sealed off to the extent possible.
Postscript: It turns out that my grandmother Sylvia highly recommended the use of spent coffee grounds which she apparently used extensively in her long, narrow backyard where she loved to garden (located near Salt Lake City's Windsor Street, meticulously arranged and care for, and of which I have fond memories). She was doing that probably since at least the 1940's, if not earlier. Hats off to our ancestors who learned these lessons long before us.